Types of ship's speed meters for measuring a ship's speed relative to the water include an electromagnetic type, an acoustic type, a rotary-wing type, etc. Among these ship's speed meters, the electromagnetic ship's speed meter measures a ship's speed relative to the water using the law of electromagnetic induction. More specifically, the electromagnetic ship's speed meter is a sensor provided to a hull, the sensor including a coil for producing a magnetic field by being excited and one pair of electrodes for detecting electromotive force. When the magnetic field around the coil is moved with respect to a conductor (e.g., seawater) as the hull moves, induced electromotive force is detected by the electrodes. Here, when the magnetic field is constant, the electromotive force is proportional to the moving speed of the magnetic field (hull). Thus, the ship's speed relative to the water can be obtained based on the magnitude of the electromotive force.
In contrast, the acoustic ship's speed meter (sometimes called “Doppler log”) measures a ship's speed relative to the water using the Doppler effect. More specifically, the acoustic ship's speed meter has a wave transmitter and a wave receiver provided to a hull. The wave transmitter and the wave receiver may be integrated or separated. In both cases, the wave transmitter emits sound waves to the bottom of water and the wave receiver detects sound waves reflected by the bottom of water or by suspended matter in water (such as plankton, garbage, etc.). Hereinafter, the bottom of water and suspended matter in water reflecting sound waves emitted from a wave transmitter will be collectively called “reflection object”.
When sound waves emitted from a hull (wave transmitter) are reflected by a reflection object and returns to the hull (wave receiver), if there is a relative speed between the hull and the reflection object, a frequency difference (fd) corresponding to the relative speed is generated between the frequency of the sound waves emitted from the wave transmitter and the sound waves detected by the wave receiver. Thus, a ship's speed relative to the water can be obtained by obtaining the frequency difference (fd) and subjecting the frequency difference (fd) to an arithmetic processing. More specifically, a frequency (fm) of a sound wave emitted from a hull (wave transmitter) and reflected by a reflection object and a frequency (fr) of a sound wave returning to the hull (wave receiver) are expressed by the following equations.
                    fm        =                ⁢                  ft          *                      C            /                          (                              C                -                                  V                  *                  cos                  ⁢                                                                          ⁢                  θ                                            )                                                              fr        =                ⁢                  fm          *                                    (                              C                +                                  V                  *                  cos                  ⁢                                                                          ⁢                  θ                                            )                        /            C                                                  =                ⁢                  ft          *                                    (                              C                +                                  V                  *                  cos                  ⁢                                                                          ⁢                  θ                                            )                        /                          (                              C                -                                  V                  *                  cos                  ⁢                                                                          ⁢                  θ                                            )                                          
Here,
ft: frequency of a sound wave emitted from a hull;
fm: frequency of sound wave observed at a reflection object;
fr: frequency of a sound wave observed again at the hull;
C: sound speed in sea water
V: ship's speed relative to the water (=current velocity)
θ: emitting angle of sound wave.
Thus, a frequency difference (fd) can be expressed as follows using the speed of a ship relative to the water.
                                                        fd              =                            ⁢                                                fr                  -                  ft                                =                                ⁢                                  ft                  *                                                            (                                              C                        +                                                  V                          *                          cos                          ⁢                                                                                                          ⁢                          θ                                                                    )                                        /                                          (                                              C                        -                                                  V                          *                                                                                                                                                                                                                            ⁢                                  cos                  ⁢                                                                          ⁢                  θ                                )                            -              ft                                                                          =                            ⁢                              2                *                V                *                ft                *                cos                ⁢                                                                  ⁢                                  θ                  /                                      (                                          C                      -                                              V                        *                        cos                        ⁢                                                                                                  ⁢                        θ                                                              )                                                                                                                          =                            ⁢                              2                *                V                *                ft                *                cos                ⁢                                                                  ⁢                                  θ                  /                  C                                ⁢                                                                  ⁢                …                ⁢                                                                  ⁢                                  (                                                            since                      ⁢                                                                                          ⁢                      C                                        ⪢                                          V                      *                      cos                      ⁢                                                                                          ⁢                      θ                                                        )                                                                                                                        ⇒                V                            =                            ⁢                                                C                  *                                                            (                                              fr                        -                        ft                                            )                                        /                                          (                                              2                        *                        ft                        *                        cos                        ⁢                                                                                                  ⁢                        θ                                            )                                                                      =                                  C                  *                                      fd                    /                                                                                                                                        ⁢                              (                                  2                  *                  ft                  *                  cos                  ⁢                                                                          ⁢                  θ                                )                                                                        Formula        ⁢                                  ⁢                  (          1          )                    
That is, by obtaining a frequency difference (fd) and subjecting the frequency difference (fd) to an arithmetic processing, a speed of a ship relative to the water can be obtained (see Tetley, L., & Calcutt, D. (2001). Chapter 3: Speed measurement. Electronic Navigation Systems (Third Edition) (Vol. 42, pp. 45-87). Elsevier Ltd.).
Here, when a hull moves in a fluid, a boundary layer is created near a surface of the hull in contact with the fluid. Influence of viscosity appears significantly in the boundary layer, making a speed gradient very large. On the other hand, the influence due to viscosity is little in an area outside the boundary layer (main course) and thus the fluid flows in almost the same manner as an ideal fluid. Thus, to obtain an accurate ship's speed relative to the water, it is needed to obtain a speed of a fluid (current velocity) outside the boundary layer.
Accordingly, there has been an existing electromagnetic ship's speed meter having a sensor provided to a tip of a measuring rod extended from a ship bottom. In addition, there has been an existing acoustic ship's speed meter for detecting a current velocity at several meters below the ship bottom.